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Efficient Algorithms for Computing Nœther Normalization

  • Amir Hashemi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5081)

Abstract

In this paper, we provide first a new algorithm for testing whether a monomial ideal is in Nœther position or not, without using its dimension, within a complexity which is quadratic in input size. Using this algorithm, we provide also a new algorithm to put an ideal in this position within an incremental (one variable after the other) random linear change of the last variables without using its dimension. We describe a modular (probabilistic) version of these algorithms for any ideal using the modular method used in [2] with some modifications. These algorithms have been implemented in the distributed library noether.lib [17] of Singular, and we evaluate their performance via some examples.

Keywords

Polynomial Ring Computer Algebra System Hilbert Series Input Size Hilbert Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Amir Hashemi
    • 1
    • 2
  1. 1.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran
  2. 2.Inria-Salsa project/ Lip6-Spiral teamParisFrance

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